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In: Statistics and Probability

compute the 90%, 95%, and 99% confidence interval for N=282 Mean= 2.36 SD= 1.19 explain the...

compute the 90%, 95%, and 99% confidence interval for N=282 Mean= 2.36 SD= 1.19

explain the effect of confidence interval on the width of the interval

Solutions

Expert Solution

a) Sample size = n = 282

Sample mean = = 2.36

Standard deviation = s = 1.19

We have to construct 90% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 282 - 1 = 281

Level of significance = 0.10

tc = 1.650 ( Using t table)

So confidence interval is ( 2.36 - 0.1169 , 2.36 + 0.1169) = > ( 2.2431 , 2.4769)

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b) Sample size = n = 282

Sample mean = = 2.36

Standard deviation = s = 1.19

We have to construct 95% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 282 - 1 = 281

Level of significance = 0.05

tc = 1.968 ( Using t table)

So confidence interval is ( 2.36 - 0.1395 , 2.36 + 0.1395) = > ( 2.2205 , 2.4995)

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c) Sample size = n = 282

Sample mean = = 2.36

Standard deviation = s = 1.19

We have to construct 99% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 282 - 1 = 281

Level of significance = 0.01

tc = 2.593 ( Using t table)

So confidence interval is ( 2.36 - 0.1838 , 2.36 + 0.1838) = > ( 2.1762 , 2.5438)

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If the confidence level increase then the width of confidence interval also increases.

orchestra answered 1 year ago
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